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Is the analemma the intersection of a sphere and a cone? - phma
The last link notes, "incorrectly claims Mercury and Venus lack analemmae". The link titled 1 also makes this claim, and states why. If the author of this comment thinks that they do, what would they look like?
The external link to the article by Brian Tung (currently dated and copyrighted 2002), is I think, important, because at the end it contains a link to a C program for the analemma or equation of time, which uses a more accurate formula than many use. Particularly, it is more complex than simply working out the Equation of Time due to the two components (eccentricity and obliquity) on their own, independantly of each other, then adding the two results. The movement of the Sun eastwards among the stars due to the orbital motion of the Earth, is itself uneven due to eccentricity of the orbit; this needs to be taken into account when working out the component of the Equation of Time due to the obliquity. As Brian Tung states in the last paragraph of his page, the formula which many use (working out the two effects independantly then adding them linearly) works reasonably well for small eccentricities and obliquities, but becomes noteably inaccurate for extreme orbits and inclinations. - Roo60 13:54, 2 Apr 2005 (UTC)
It is not correct that the analemma would be a straight line if the orbit were circular but the axis tilted as it is. It is true that if the axial tilt were only slight, then the analemma would be almost a straight north-to-south line; but with very great axial tilts, the figure-of-eight feature would be very marked indeed.
As is explained in the article Equation of time, when the sun is crossing the equator (at the time of the equinoxes), then it is climbing/lowering at a 23.44° angle, which means that for every 1.09° of actual motion along the celestial sphere, it only moves eastwards in Right ascension by 1°. Conversely, at the solstices, the sun is cutting across meridians, meaning that for every 1° of motion along the plane of the ecliptic, its Right ascension increases by 1.09°. Thus, the Equation of time follows two cycles per year. - Roo60 20:05, 2005 Apr 7 (UTC)
There's a group of amateur astronomers in Virginia called the Analemma Society. I don't know if it's wworthy of mention so I'm just putting it here: http://www.analemma.org/ -- Howdybob 21:11, 16 July 2006 (UTC)
Just a comment on the photo of the analemma with the dates drawn in. The cross-over of the figure of eight is marked 15/3 and 1/9. Surely it should be 15/4 and 1/9 which is when the Equation of Time is zero (its graph crosses the x-axis). - Panus
Someone please rewrite constant reference to 'figure 8'; I don't know how to do it in a plausible way. Alexander Iwaschkin 03:25, 23 January 2007 (UTC)
Most globes in days of yore used to have analemmas printed on them as well as an ecliptic circle printed about the globe intersecting the equator. Since most globes these days no longer come with these features, I have been looking "on line" for a good diagram of the analemma which I could print out and use to roughly detiremine the declination of the sun any time of year. I had hoped to find one here, but no. Nor, can I find a link to one! There must be a good analemma diagram somewhere to be seen, but I haven't found one yet. (By good, I mean: not distorted, and showing the months broken down to five day intrevals or less, along the line of the analemma, which would enable one, for any given date to detiremine with reasonable accuracy the declination of the sun, together with it's time ahead or behind mean solar time. I know there are tables that do this; but, the analemma is a nifty graphic tool that accomplishes this in one simple diagram. —Preceding unsigned comment added by 4.178.15.111 ( talk) 21:52, 9 January 2008 (UTC)
"The width of the analemma is a result of the ellipticity of the earths orbit. Please explain how this relates to vibration in universal joints."
The "figure-8" related East-West motion in the analemma has absolutely nothing to do with the eccentricity of the Earth's orbit. Eccentricity causes a 12 month period East-West motion, not a 6 month period! It distorts the "figure-8". The "figure-8" East-West motion is due to the tilt of the Earth's axis. Assuming a circular orbit for simplicity, the 24 hour strobed position of the sun follows a great circle across the earth with constant velocity and one year period. During the equinoxes this sun circle crosses the equator at an angle, so it's eastward movement is slower that the 24-hour strobed rotation of the Earth. During the solstices the sun is moving parallel to the equator, and since by defintion of the solar day they must have the same yearly average, it is moving faster that the Earth's eastward rotation.
Likewise the vibration in a universal joint is due to the tilt in the coupled angular motion. The vibration also has a 2X frequency. The equations are the same! —Preceding unsigned comment added by Cloudswrest ( talk • contribs) 18:31, 10 September 2008 (UTC)
OK, fair enough. At bottom, the analemma is the projection of one angular rotation onto another, off axis angular rotation of the same frequency. In the case of the earth the two "rotations" are the yearly motion of the sun around the ecliptic, and the 24 hour strobed rotation of the earth, which also has a yearly period. The 24-hour strobed rotation of the earth is about 1 degree per day. A sidereal day (star meridian crossing to crossing) is less than a solar day, 23 hours, 56 minutes. A sidereal day is 360 degrees of earth rotation, a solar day is 361 degrees of earth rotation. The "off axis" in this case is of course the earth's tilt of 23.44°.
In the case of two coupled drive shafts, if you were to paint a dot on the rim of one, and observe this dot from the corresponding point on the rim of the other, there are two cases. In the case of a hyphoid gear coupling or CV joint, both shafts have constant rotation velocity and the dot would trace out a perfect analemma. In the case of a universal joint coupling, the driven shaft, although sychronous, has to speed up and slow down at a 2X rate in order to "cancel" the analemma. The dot appears to just move up and down from the view of the driver shaft. This is the sourse of the second harmonic vibration.--
Cloudswrest (
talk)
16:30, 11 September 2008 (UTC)
Possibly interesting: this page of mine illustrates how the interrelation of tilt and eccentricity affects the shape of the analemma. — Tamfang ( talk) 04:52, 30 July 2010 (UTC)
I was in a public square in Bristol some time ago and I noticed an odd pattern of marks on the ground. After wandering round puzzling about it I realised it must be something to do with the sun's shadow, probably at noon, cast from the top of a sculpture at one end that looked a bit like a spine, since there was a far off mark which looked about right for the winter solstice and a near one that looked right for the summer, and a figure of eight which crossed at where I concluded a shadow was cast at the equinoxes. After thinking this was a pretty cool thing to put in a town square I set about trying to find out more, and came across this word "analemma". My question then, is whether such a representation of the analemma from a year's worth of shadows can also be referred to as an analemma, and if so whether this example is anything notable that might merit a mention in the article, or whether there are plenty of these around the world. If anyone wants to see it, have a look at an aerial photo from Google Maps. 79.64.181.148 ( talk) 19:55, 2 March 2009 (UTC)
I've just established that this is Millennium Square, which has a stub. You can see some of the analemma markings (the discs on the ground) in this photo I've found on Commons. Can someone familiar with the terminology add a note about this interesting feature of the square to its article. It might solve a mystery for anyone who looks the square up! 79.64.181.148 ( talk) 20:01, 2 March 2009 (UTC)
Thumbnail size images add nothing to this article as they do not illustrate the text. I suggest this is a case where it is appropriate to force Image size as per the Manual of Style, Wikipedia:Manual_of_Style#Images . Lumos3 ( talk) 23:50, 25 March 2009 (UTC)
The poem added by Mushlack on 5 December 2009 is from Analemma in Verse by Tad Dunne. Because no release from copyright is mentioned by Dunne and it was composed about 1996, the poem is under copyright in virtually all countries and it is thus a copyright violation to include it in Wikipedia. I am removing the offending poem. I am adding an external link to the poem, which is permitted for a work under copyright. — Joe Kress ( talk) 20:30, 20 December 2009 (UTC)
Clarification: Even an external link is not permitted per WP:COPYLINK if an editor knows that the site violates the copyright holder's copyright. In this case, the author of the poem placed it online. — Joe Kress ( talk) 06:38, 21 December 2009 (UTC)
I have removed the merger proposal since it no longer applies.-- Lasunncty ( talk) 11:11, 19 January 2010 (UTC)
The analemma represents a completely worthless exercise and only emerged in the late 17th century along with mechanical clocks so that giving significance to a wandering Sun 'analemma' by gauging its position using the average 24 hour day would be a harmless exercise until empiricists decided to explain the observation using the Earth's daily and orbital motions.There is only room in the celestial arena for the true 'wanderers' - the planets,and it was Copernicus who explained the 'wandering' motions including retrogrades by determining that the Earth's own orbital motion resolved the observations.The idea of a wandering analemma Sun let alone explaining it by way of planetary dynamics is hideous,don't take my word for it,extract the details from the great astronomer himself - "Moreover, we see the other five planets also retrograde at times, and stationary at either end [of the regression]. And whereas the sun always advances along its own direct path, they wander in various ways, straying sometimes to the south and sometimes to the north; that is why they are called "planets" [wanderers]. Copernicus
In short,the astronomical version of the 'Piltdown man' skull is the analemma and the reason it emerged is far more interesting,for all the wrong reasons,than this short description would imply. Oriel36 ( talk) 20:11, 19 June 2010 (UTC)
I think it is utter nonsense too,people who believe something as childish as gauging a wandering 'analemma' Sun using a 24 hour clock and then going on to explain it using planetary dynamics may be the most stupid people on the planet. —Preceding unsigned comment added by Oriel36 ( talk • contribs) 19:35, 20 June 2010 (UTC)
I knew what you were saying but like so many others,you have no answer to the statement of Copernicus which forbids the idea of a wandering 'analemma' Sun in the same celestial arena as the 'wandering' planets ,this wandering motion was resolved by the Earth's own orbital motion - http://apod.nasa.gov/apod/ap011220.html . If astronomy has a 'Piltdown man' skull then the analemma certainly is that, as a matter of substance ,the thing is somewhere between the Loch Ness Monster and intellectual oblivion. Oriel36 ( talk) 05:29, 21 June 2010 (UTC)
Ah,my Tamfang shadow,I was wondering when you would show up. I consider the analemma too embarrassing in the same way all hoaxes are,it was a means to an end in attempting to shift daily rotation away from its determination at natural noon by having the Sun wander all over the place,sideways and up and down and it would be funny only that people are dead serious about it. The determination of natural noon by the use of a shadow in reflecting the daily rotation and orbital motion of the Earth has no up and down component, just a simple alignment and a straightforward determination which Huygens relates with clarity - "Draw a Meridian line upon a floor and then hang two plummets, each by a small thred or wire, directly over the said Meridian, at the distance of some 2. feet or more one from the other, as the smalness of the thred will admit. When the middle of the Sun (the Eye being placed so, as to bring both the threds into one line) appears to be in the same line exactly you are then immediately to set the Watch, not precisely to the hour of 12. but by so much less, as is the Aequation of the day by the Table." http://www.xs4all.nl/~adcs/Huygens/06/kort-E.html Oriel36 92.251.255.11 ( talk) 08:15, 31 July 2010 (UTC)
I have to laugh at "Huygens-noon" in inverted commas,Huygens was relating an ancient observation that the natural noon cycles vary hence the equable 24 hour day as a human devised derivative along with terms such as AM and PM that still retains the correlation between natural and 24 hour clock noon.Of course,if you are an analemma addict,you couldn't possibly comprehend what causes the natural noon cycles to vary as it shares a common mechanism with the terrestrial effect where temperatures fluctuate across the solstices. Oriel36 ( talk) 17:00, 4 August 2010 (UTC)
. The spin of the earth during the year is fairly constant, however, the orbit around the sun is not circular, so its apparent (and actual) orbital speed varies, decreasing twice each year, for 3 months, as it 'climbs' from proximity to extremity, each followed by 3 months of acceleration back to the next proximity. As the earth recedes, the sun appears to 'fall behind in the noonday sun'. As it approaches the sun again, it catches up again, averaging out 'just right'.
. If you divide the year by the number of days (D), to get average the number of seconds per day (N), and take a vertical photo of the sky every S seconds, you would see the sun wander slightly (a couple of degrees) east & west across the sky every 6 months.
. This slight & consistent effect (nothing to do with obvious & complex 'Planetary' wandering) is not caused by any actual sun motion, and is the major cause of the analemma's width.
. While taking these photos, you might also take night photos S/2 seconds later, and see that the stars are moving across the night sky very steadily at 360/D, without E-W wander.
. I think this is the main reason and clearest explanation of why the analemma is not just a line.
. However, more subtly, the tilt of earth's axis does not align with either axis of it's elliptical orbit, and the planets also have subtle gravitational and perhaps detectable electric coupling effects, adding spice to the planetary complex.
The sun may tremble under the minuscule tugs of its planets, and its 'wanderings' are of galactic proportions, but both are well beyond the perception of all but the most extreme telescopes.
Wikidity (
talk)
22:15, 2 August 2010 (UTC)
Here is what you do,there is an excellent article from about 1917 about something that was stitched together to make it look biologically feasible,the astronomical 'analemma' version doesn't even have the pleasure of being remotely elaborate but exists as something so crude that it is almost impossible to comment on other than an attempt to denote the position of the Sun using a 24 hour day and a watch. http://www.jstor.org/pss/2788903 Oriel36 ( talk) 17:46, 4 August 2010 (UTC)
The transition from AM to PM represents a global event along the same meridian line hence the 'M' in the abbreviation,it does not matter what hemisphere of the Earth you reside in,when the shadows align along the meridian as Huygens clearly explains, natural noon is determined the same way each cycle along with its adjustment to 24 hour noon.It is not rocket science,there is no 'analemma' feature to consider with no planetary dynamics needed to explain it - "Draw a Meridian line upon a floor and then hang two plummets, each by a small thred or wire, directly over the said Meridian, at the distance of some 2. feet or more one from the other, as the smalness of the thred will admit. When the middle of the Sun (the Eye being placed so, as to bring both the threds into one line) appears to be in the same line exactly you are then immediately to set the Watch, not precisely to the hour of 12. but by so much less, as is the Aequation of the day by the Table." Huygens Oriel36 ( talk) 19:29, 5 August 2010 (UTC)
The description about the "first analemma photograph" is not quite correct. The National Geographic blurb has a couple mistakes as well. I haven't seen the original Sky & Telescope article the photo appeared in (June 1979), but I did find an annotated version of the photo here. I also found a good description here (albeit in Georgian). However, these sites are not primary sources, and I'm not sure if their source is the original S&T article or something else. -- Lasunncty ( talk) 06:41, 2 January 2011 (UTC)
At the end of the article, there is a link to "The Use of the Analemma — from an inset from Bowles's New and Accurate Map of the World (1780)". This refers to the (English) meaning of "analemma" in the 18th century. At that point in time an analemma was an orthographic projection of the sphere --an entirely distinct definition (so the link probably doesn't belong here). This "analemma" could be a carefully drafted drawing or, in fact, a device for calculation, like a graphical slide rule. These "analemmas" were used to get approximate solutions to the various problems of spherical trigonometry. Only after c.1800, globe makers began placing charts of the Sun's declination on globes and labeling these as analemmas. These are the origin of the modern usage of the word analemma. Also many of these early analemmas did not include the graphing of the equation of time hence they were oval instead of "figure 8" shaped. This is described well in most early 19th century guides to the "use of globes". For example in Keith's "New Treatise on the Use of Globes" published in New York in 1819, you will find
Keith's "Use of Globes" is available through Google Books.
As recently as 1910, some "analemmas" on globes were ovals because they only charted declination and not also equation of time. Whether the globe-maker Cary can be credited with the invention of the modern analemma (and re-definition of the word) or not, I don't know but it seems likely. Someone would have to find a source for that, so I'm just leaving on this on the talk page. 173.105.173.249 ( talk) 04:56, 26 May 2011 (UTC)
The gentleman should be satisfied with the references which demonstrate that the 'wandering Sun' analemma was a tragic and inevitable consequence of the attempt to fit the Earth's daily and orbital motions into right ascension by guys in the late 17th century and I leave those references on the page as a resource,nothing more or less. Gkell1 ( talk) 05:59, 9 July 2011 (UTC)
It would be super if this article could explain how Tom Hanks was able to make an analemma and use it to navigate off of the island! There's a link from the "Cast Away", 2000, article to the analemma article, but nothing in the analemma article explains in simple terms what a person would do to create an analemma and use it for survival navigation.
You never know when information like that will come in handy...~~
~~ — Preceding unsigned comment added by Entwhiz ( talk • contribs) 11:34, 18 February 2012 (UTC)
There is a graph supposedly showing sunrises for the month of January, 2008 for Gabon. The x-axis is date (with dates ranging from 01/01 to 01/09 then back to 01/01 !!!!). This is garbage. This graph is so flawed that it should be removed. I missed the place in the article (if it exists) where this graph was used to further the article. Assuming that the point of the graph is to show the two maxima and minima in early January, it is still completely wrong to graph a continuous line. From this graph I can determine that sunrise on 01/02 is 06:34.00 and that 8 hours later (⅓ of a day) sunrise is at 06:34.5 - This is simply absolutely wrong. (of course due to the poor quality of the graph, I do not know whether this is local time, GMT or what (ok, I admit that I don't know if Gabon is GMT or what, either)). → Please remove this graph, until it is corrected. Sunrise is a DISCRETE phenomenon (at a given location). It only happens once a day (at a given location). The graph is rubbish. 173.189.74.6 ( talk) 17:55, 21 September 2013 (UTC)
"Mercury: Because orbital resonance makes the day exactly two years long"
This appears wrong, since the resonance is 3:2 and not 1:2. The conclusion therefore also seems wrong. Can anyone with more experience in this take a look? 07:41, 7 February 2019 (UTC) — Preceding unsigned comment added by 2001:2012:406:0:60AE:6009:1576:404C ( talk)
In the second paragraph, the following sentences don't make sense: "The mean position appears to revolve around the Earth once every mean solar day, because of the Earth's rotation. This daily revolution is not considered to be averaged out to get the mean. The mean position of the Sun is therefore at the same place in the sky at the same time every day, but not at other times."
I suggest deleting them. Instead I would insert "at a fixed time" in the preceding sentence after "an observer at a fixed point on the Earth" — Preceding unsigned comment added by 137.108.145.24 ( talk) 2015-01-30T14:44:24
I did not write the above, but I agree with it. The first 2 paragraphs are very unsatisfactory and should certainly be deleted. The last sentence of the 2nd paragraph is the only correct thing there. The reference to a mean position on the celestial sphere is entirely wrong. Whoever wrote this has a very confused notion of what the analemma is. I have therefore deleted the first 2 paragraphs, and have written an alternative. I am not a professional astronomer, so what I have written may need to be revised, but I am confident that this new lead is better than what was there before. g4oep — Preceding unsigned comment added by 77.96.58.212 ( talk) 2015-05-17T02:22:27
Would someone like to enlarge on this : "The figure-eight form arises from the relationship between the direction of the earth's axis, and the line passing through the perihelion and aphelion of the earth's elliptical orbit around the sun." It would be interesting to know under what conditions the analemma would be a line inclined to the ecliptic meridians, and when it would be a circle. i.e. - how is the phase of the equation of time relative to the solar declination determined ? It seems to me that the analemma is an example of a Lissajous figure, the figure 8 form being related to the large 2nd harmonic content of the equation of time. How does this 2nd harmonic arise ? Under what conditions would it be minimised, and is it possible that under some conditions higher harmonics could be present, giving 3 or more loops ? g4oep — Preceding unsigned comment added by 77.96.58.212 ( talk) 2015-05-18T02:04:11
Thank you. I feel that the lead is steadily improving as these contributions accumulate. I have made a slight edit to the sentence concerning the long axis of the analemma in order to pull it into greater accord with what I think you mean. This sentence has now moved away from the idea I had when I wrote it - namely to give some meaning to the line of the long axis. Can anyone identify this line ? Is it a line of celestial longitude, for example ? Also, any comments on my immediately preceding edit on this page concerning Lissajous figure, conditions for specific phase relationships (zero phase, phase quadrature), harmonic content ? Concerning the idea of the movement of the analemma, as I see it, the analemma is a fixed pattern in the sky representing the sun's apparent motion as seen under the conditions stated in the article. The figure will appear at different positions in the sky if the chosen time of day at which the observations are made changes. I think a difficulty will arise if you attempt to define the analemma in such a way that, as a whole, it can move continuously, following the daily path of the sun in the sky, or, as was originally indicated, being fixed relative to the celestial sphere and therefore showing diurnal movement. For example, the line drawn in the sky by the sun on a particular day will be a continuous curve, and on successive days through the year discreet curves will appear. But a collection of such lines will not be an analemma, nor will the supposed problem of the analemma as a collection of discreet points be solved in this way. I would suggest that the analemma is in fact a collection of points, and the supposed continuous line of the figure exists only in the imagination. Wikki has a policy of presenting what is considered to be the usual meaning of terms, so I would like to ask "how is the analemma usually understood: as a fixed pattern of discreet points or as a moving pattern formed from a continuous line ?"
On reflection, I can see that a continuous curve would result if the analemma were defined as a plot of solar declination against the equation of time (as mentioned in the article). But it now seems that these are alternative definitions, related, but non-equivalent. Perhaps both should be given as non-equivalent alternative definitions: one a pattern in the sky, the other a plot on a graph. Of course neither would move in the sense we are discussing. G4oep ( talk)
Good - the article is steadily improving. One minor point - I don't like to argue over trivia, but I think that precise use of language is desirable. This is one of the definitions of "axis" given here: http://www.thefreedictionary.com/axis. "2. Mathematics: a. An unlimited line, half-line, or line segment serving to orient a space or a geometric object, especially a line about which the object is symmetric". This is the meaning I had in mind, including the "unlimited" part. It makes no sense to me to say that an unlimited line is bisected, but I can appreciate the meaning of the bisection of the figure along an axis which is itself unlimited. You say that the figure is not bisected, so I cannot follow your meaning. I am sure that we agree that the figure has equal angular extent above and below the celestial equator. Can we find a form of words that sorts out this difficulty as well ? I would still like to include a comment about the orientation of this axis, and, if possible, its relationship to some form of recognised co-ordinate system. G4oep ( talk)
The only reason for the figure 8 pattern is the axial tilt. The horizontal asymmetry stems from the misalignment of the solstices and apsides. It is not possible to have three or more loops.
The analemma is continuous. The discrete-point version only arises from the usual method of photographing it.
The origin of the graph is the position of the mean sun. Thus the analemma moves around the celestial sphere once per year.
A line connecting the northernmost point and the southernmost point of the analemma is meaningless. It is not perfectly vertical, nor does it divide the analemma into equal halves. If however you are talking about the y-axis of the graph, that represents when the equation of time is zero, or when the real sun would be at the same right ascension as the mean sun.
--
Lasunncty (
talk)
12:16, 21 May 2015 (UTC)
I removed "(mostly in items 5 and 6 of the table of contents)" from the second paragraph of the introduction, because future edits, could change where in the table of contents those topics fall. An editor who adds a new section could easily not notice that they need to change these two numbers. And, since this comment is parenthetical, it is not essential to the meaning Nick Beeson ( talk) 04:46, 7 June 2015 (UTC) of the sentence.
seems Analemma means: “pedestal of a sundial".
Saw it in the italian wikipedia and also here, as third explanation:
http://www.yourdictionary.com/analemma Hexagone59 ( talk) 00:25, 21 November 2015 (UTC)
Note that the width (east-west component) of the eight-figure of analemma requires only an axial tilt. The effects of eccentricity (for the case of Earth) manifest primarily in a tilt of analemma, asymmetry of the lobes and a slight right-left assymetry. Please keep that in mind editing contributions of orbital parameters to the shape of analemma. L3erdnik ( talk) 18:48, 4 July 2017 (UTC)
I plan to edit some things not to upset those writers who have made the article what it is, but to make it more accessible to the average reader. Bear with me if I make a mistake. I am having trouble with the concept "East-west motion could come from either eccentricity or axial tilt on their own" ... after struggling with it, I can conceive how eccentricity yields the e-w effect, but not how axial tilt yields the e-w effect. There in fact seems to be an existing puzzle in the "description" section, which says "Viewed from an object with a perfectly circular orbit and no axial tilt, the Sun would always appear [to be] be a dot" ... but also says "with a circular orbit but significant axial tilt, the analemma would be a figure of eight"... and then says "with an eccentric orbit but no axial tilt, the analemma would be a straight east–west line" The problem with comprehending that is that the middle statement [circular with tilt] would be expected to say "a straight up and down line" with no east-west component. Carlw4514 —Preceding undated comment added 11:29, 13 January 2018 (UTC)
I think the statement "The asymmetry ... arises ... from the fact that the equinoxes do not occur at the perihelion and aphelion" is incorrect. You can have an orbit in which equinoxes do not occur at the perihelion and aphelion and with a perfectly symmetric analemma. One needs only to look at the two components of the Equation of Time to grasp this concept. Just slide one of the two curves by a few days, and the equinoxes still do not occur at the perihelion/aphelion, but the resulting analemma will be perfectly symmetric.-- Gciriani ( talk) 14:56, 13 January 2018 (UTC)
I'm including for reference links with simulations for equinox at 90 degrees and equinox at 0 degrees. The relative contributions of tilt and eccentricity are approximately in the same proportion as for the earth, where the effect of eccentricity is about 80% of the effect caused by tilt.-- Gciriani ( talk) 05:07, 18 January 2018 (UTC)
I removed these sentences from the other planets section, but was then reverted:
The source used to support these sentences was already in question, and plus there is already discussion about the shape of the analemma earlier in the article. What I can tell from simulations is that a loop occurs only when obliquity is low and the angle between apsides and equinoxes is high. Eccentricity only has a minor effect. The teardrop is a transitional state between the elliptical loop and the figure-eight. -- Lasunncty ( talk) 17:05, 25 January 2018 (UTC)